Supplementary Materials and Methods for
Enhanced air pollution via aerosol-boundary layer feedback in China
T. Petäjä1*, L. Järvi1, V.-M. Kerminen1, A. Ding2*, J. Sun2, W. Nie1,2, J. Kujansuu1, A. Virkkula2,3,
X. Yang2, C. Fu2, S. Zilitinkevich1,3,4 and M. Kulmala1*
1
Department of Physics, University of Helsinki, Finland
2
Institute for Climate and Global Change Research & School of Atmospheric Sciences, Nanjing
University, China
3
Finnish Meteorological Institute, Helsinki, Finland
4
University of Nizhny Novgorod, Russia
*Correspondence to: tuukka.petaja@helsinki.fi, dingaj@nju.edu.cn, markku.kulmala@helsinki.fi
A1 Theoretical derivation of boundary layer height in polluted urban convective boundary
layer
A1.1 Energy balance
The energy balance at the Earth surface reads (in W m-2):
𝐹 ∗ + 𝐹𝐴 = 𝐹𝐻 + 𝐹𝐸 + 𝐹𝑆 ,
(SI-1)
where 𝐹 ∗ is the net radiation flux resulted from counteraction of solar and long-wave radiation
fluxes, both of which consists of the upward and downward components; 𝐹𝐴 is positive (upward)
energy flux due to anthropogenic heating of urban infrastructures; 𝐹𝐻 and 𝐹𝐸 are turbulent fluxes of
sensible and latent heat; and 𝐹𝑆 is the net-storage heat flux. New advection is assumed to be
negligible when compared to the other components.
The difference Δ𝐹 ∗ between the values of the net radiation flux in the non-polluted and polluted
atmosphere leaves the anthropogenic heating unchanged, and causes variations ∆𝐹𝐻 , ∆𝐹𝐸 and ∆𝐹𝑆
in all fluxes on the right hand side of Eq. (SI-1):
∆𝐹 ∗ = ∆𝐹𝐻 + ∆𝐹𝐸 + ∆𝐹𝑆 ≈ ∆𝐹𝐻 + ∆𝐹𝐸 .
(SI-2)
Here, the variation ∆𝐹𝑆 in the net-storage heat flux is neglected as small compared to the major
variations: ∆𝐹𝐻 and/or ∆𝐹𝐸 ; and the sum ∆𝐹𝐻 + ∆𝐹𝐸 represents the total turbulent heat-flux
decrement caused by the air pollution. Clearly, the net radiation flux approaching the surface is
smaller in the polluted atmosphere, so that ∆𝐹 ∗ < 0.
The major driving forth of the growth of convective BL is the near-surface value of the vertical
𝑔
turbulent flux of the buoyancy b defined as 𝑏 = 𝑇 𝜃 + 0.61𝑔𝑞, where g is the acceleration due to
0
gravity, 𝑇0 is the reference value of absolute temperature, θ is the potential temperature, and q is
specific humidity. The buoyancy flux is expressed through the heat fluxes 𝐹𝐻 and 𝐹𝐸 :
𝐹𝑏 = 𝑐
𝑔
𝑝 𝜚𝑇0
(𝐹𝐻 +
0.61 𝑐𝑝 𝑇0
𝐿𝐸
𝐹𝐸 ) ≈ 𝑐
𝑔
𝑝 𝜚𝑇0
(𝐹𝐻 + 0.07𝐹𝐸 ),
(SI-3)
where 𝜚 is the air density, 𝑐𝑝 is the heat capacity at constant pressure, and 𝐿𝐸 is the latent heat of
condensation.
As follows from (SI-2) and (SI-3), to a rough approximation the decrement in the buoyancy flux
∆𝐹𝑏 caused by the air pollution can be taken to be proportional to the easily measurable ∆𝐹 ∗ .
A1.2 Characteristic height of urban convective BL as dependent on the surface buoyancy flux
A typical well-mixed urban convective BL grows from the city border along the wind, according to
the prognostic equation:
𝑑ℎ
𝐹
𝑈 𝑑𝑥 = 𝑎 𝑁2𝑏ℎ ,
(SI-4)
where h is the BL height, x is the distance from the border, U is horizontal wind speed at the BL
upper boundary, a is a dimensionless coefficient to be determined experimentally, and 𝑁 =
√𝜕𝑏/𝜕𝑧 is the Brunt-Väisälä frequency in the free troposphere (37). If no relevant data is available,
N can be taken equal to its typical climatological value for given city and given month. A
reasonable rough estimate is N ≈ 10-2 s-1.
̅̅̅̅̅̅ is defined as the Reynolds-averaged product of
The vertical turbulent flux of buoyancy 𝐹𝑏 = 𝑏′𝑤′
fluctuations of vertical wind velocity (𝑤′) and buoyancy (𝑏′). In the CBL, 𝐹𝑏 is positive, which
corresponds to the upward energy transport. In our analyses, this flux is determined directly from
̅̅̅̅̅̅; and it is
measurements of turbulent fluxes of potential temperature ̅̅̅̅̅̅
𝑤′𝜃′ and specific humidity 𝑤′𝑞′
demonstrated that 𝐹𝑏 essentially reduces in the polluted atmosphere.
Integrating Eq. (SI-4) yields:
𝐹 𝑥
𝐹 𝐷
ℎ = √2𝑎 𝑁𝑏2 𝑈 ≈ √2𝑎 𝑁𝑏2 𝑈 ,
(SI-5)
where D is the horizontal city scale. The approximate relation (employing D as a characteristic
distance) serves as a characteristic urban BL height. According to Eq. (SI-5), the ratio of the heights
of the polluted and non-polluted urban convective BLs is equal to the square root of the ratio of the
corresponding surface buoyancy fluxes:
ℎ𝑝𝑜𝑙𝑙
ℎ𝑛𝑜𝑛𝑝𝑜𝑙𝑙
= √𝐹
𝐹𝑏,𝑝𝑜𝑙𝑙
𝑏,𝑛𝑜𝑛𝑝𝑜𝑙𝑙
.
(SI-6)
In windy weather, U is the speed of the background wind driven by the synoptic-scale pressure
gradient. In calm weather, when the background wind is weak, the dominant role turns to the cityscale convective circulation cell driven by the urban heat island. Such cell produces its own
convective wind estimated as
𝑈~ 𝐴(𝐹𝑏 ℎ)1/3,
(SI-7)
where the combination (𝐹𝑏 ℎ)1/3 is the Deardorff convective velocity scale, and A ~ D/h is the
urban-cell aspect ratio that is essentially larger than unity. Then, substituting Eq. (SI-5) for U into
Eq. (SI-6), yields the following alternative characteristic urban BL height:
2/3
ℎ ≈ (2𝑎
𝐹𝑏
𝐷
𝐴𝑁 2
3/7
)
,
(SI-8)
2/7
which implies a weaker than square root dependence: h ~ 𝐹𝑏
.
A2 Correlation analysis
Table 1 presents the correlation analysis for the radiation and flux parameters during the 8 month
measurement period in Nanjing. The data presents cases when ambient RH is below 50% where the
effect of hygroscopic water uptake of the aerosol particles remains small (36).
Supplementary Table 1. Linear fits and associated correlation coefficients (R) between a) the
aerosol mass (PM2.5) and b) BC concentration against the different radiation and flux components
(y = a0x + a1). N is the number of data points.
a) PM2.5
RH<100%
RH<80%
RH<60%
b) BC
RH<100%
RH<80%
RH<60%
a0
a1
N
R
Kdown/Ktop
Ldown/Ktop
Q*/Ktop
Fb/Ktop
Kdown/Ktop
Ldown/Ktop
Q*/Ktop
Fb/Ktop
Kdown/Ktop
Ldown/Ktop
Q*/Ktop
Fb/Ktop
-3.31510-4
2.23110-4
-4.92910-4
-1.59410-7
-3.04910-4
1.42910-4
-5.23710-4
-1.81310-7
-6.14410-4
1.47410-4
-7.44110-4
-2.08710-7
0.537
0.348
0.385
4.88910-5
0.5705
0.3529
0.410
5.2210-5
0.653
0.350
0.460
5.69910-5
826
826
826
767
750
750
750
695
463
463
463
432
-0.07
0.22
-0.15
-0.34
-0.07
0.13
-0.17
-0.37
-0.16
0.11
-0.27
-0.36
Kdown/Ktop
Ldown/Ktop
Q*/Ktop
Fb/Ktop
Kdown/Ktop
Ldown/Ktop
Q*/Ktop
Fb/Ktop
Kdown/Ktop
Ldown/Ktop
Q*/Ktop
Fb/Ktop
-9.07410-3
3.94210-3
-11.49510-3
-3.16410-6
-8.26810-3
2.98110-3
-11.55310-3
-3.29510-6
-12.34810-3
2.11810-3
-15.70910-3
-3.96210-6
0.538
0.350
0.385
4.8410-5
0.573
0.353
0.410
5.1010-5
0.654
0.351
0.461
5.6310-5
837
837
837
777
754
754
754
699
460
460
460
429
-0.09
0.19
-0.17
-0.33
-0.09
0.14
-0.19
-0.35
-0.17
0.08
-0.29
-0.35
Fig. A1. Change in normalized a) solar radiation, b) longwave radiation, c) net all wavelength
radiation and d) turbulent vertical flux of virtual temperature as a function of observed PM2.5
concentration. Ktop is the solar radiation at the top of the atmosphere (W m-2). Only daytime
conditions from the non-rainy periods between 10:00 and 14:00 local time are considered. The
colour of the data points indicate observed relative humidity.
Fig. A2. A change in normalized a) solar radiation, b) longwave radiation, c) net all wavelength
radiation and d) turbulent vertical flux of virtual temperature as a function of observed BC
concentration. Ktop is the solar radiation at the top of the atmosphere (W m-2). Only daytime
conditions from the non-rainy periods between 10:00 and 14:00 local time are considered. The
colour of the data points indicate observed relative humidity.